^3/ 



m 551 

. C34 H /'' 

:opy 1 SvERY MAN HIS OWN 



Civil Engineer .# Surveyor 

A Manual in Two Parts. 



PART I. 

The Principles and Practice of 
LEVELING. 



Containing- rules and examples for coinpulinj;- the 
cubical contents of ditches, etc., and for estimat- 
ing" the work. 



PART II. 
Practical Hints on 

LAND SURVEYING. 



Showing- how the jniblic lands are surveved, and 
how every man may do his own surveying. 



J ^ SMITH CASTERLINE, C. E. 
r^i 1895- 

Vv 4 ■ 



LIBRARY OF CONGRESS. 



Slielf..:G-3.fT 



UNITED STATES OF AMEEICA. 



Entered according- to Act of Congress in the year 1895, b^' 

SMITH CASTERLINE, 
In the office of the Librarian of Congress at Washington. 



E. S. HUFFMAN, 

PRINTER, 
HARTFORD CITY. 



CONTENTS. 

PART I. 

PAGE 

Leveling and the Level 3 

Tripod No. 1 4 

The Sig-hts 6 

To set up the Level 6 

To adj List the Bubble 7 

The Leveling- Staff 9 

How to read the Staff 11 

The principles of Leveling- 12 

Case 1 12 

Principles of Case 1 12 

Prin. 1 12 

Prin. 2 12 

Case 2 12 

Example 13 

Principles of Case 2 14 

Prin. 1 14 

Prin. 2 14 

Explanation of Sig-ns 14 

Case 3 15 

Example 15 

Principles of Case 3 15 

Prin. 1 15 

Prin. 2: 16 

Prin. 3 17 

Drain ag-e Leveling 17 

The Grade line how Established 19 

Chang*- of Grade 20 

To find the Depth of Cutting 21 

B-nch Marks 21 

To find the Grade from a Bench 21 

Examples 22 

Example of Field Notes 23 

Drawint:" a Profile 23 

(xrafle Stakes and their Use 25 



CONTENTS. 

PAGE 

■The Grade Slakes as a Ivevel 27 

Width of Ditches how Computed 29 

Kxcavation how Computed 29 

Table 29 

General Rule 31 

For Ditches that are to be Tiled 32 

Rule 32 

The Work of Excavating- how Estimated 32 

PART II. 

The Compass 34 

Spirit Levels how Attached 36 

To Adjust the Levels 37 

Tripod No, 2 37 

To Set up the Compass 40 

The Chain 41 

Marking- Pins 42 

Instructions on Chaining- 42 

Practice with the Compass 44 

Case 1 44 

Case 2 45 

Case 3 46 

Case 4 46 

Rule for Correcting- the Stakes 47 

Case 5 48 

Case 6 50 

Orig-inal Survey 51 

Subdivisions of Sections and Method of 

Estalishing- Corners 55 

Table for Land Measure 58 

To Reduce Chains to Feet 58 

To Reduce Feet to Chains 58 

To Reduce Chains to Rods 59 

To Reduce Rods to Chains 59 

Computation of Area 59 

Examples 59-62 

Division of Eand 62 

Examples 62-65 

Abstract of Decisions 66 



EVERY MAN HIS OWN 



Civil Engineer .0 Surveyor 

A Manual in Two Parts. 



PART I. 

The Principles and Practice of 
LEVEUNQ. 



Containing- rules and examples fcr computing- tlie 

cubical contents of ditches, etc., and for estimat- 

inir the work. 




PART II. /l^^-' V " - 
Practical Hintdivui ^uj^c- 

LAND surveying: 



Showing- how^ the public lands are surveyed, and 
how ever}' man may do his own surve^'ing*. 

-BY— 

/ 
SMITH CASTERLINE, C. E. 

1895- I 



G 



m 

JO li 

^ PREFACE. 



f^ 



It is g-enerally supposed that to understand 
the practice of leveling- and surveying-, one 
must be well versed in the hig-her branches of 
mathematics and provided with costly instru- 
ments. This IS necessary if the object of the 
learner is to fit himself for a thoroug*h, prac- 
tical eng-ineer. But the object soug-ht by the 
author of this little book, is to so simplify the 
principles of leveling and surveying that any 
one, having- a very limited knowledg-e of math- 
ematics, can understand and practice them; 
and it is desig-ned for the use of farmers, con- 
tractors of earth-work and practical ditchers; 
whereby they will be enabled to do their own 
surveying and leveling, and estimate their 
own work. 

Many hard earned dollars have been paid 
to engineers for leveling-, that mig-ht have 
been saved to the farmer, and others, for want 
of the knowledg-e contained herein; and thous- 
ands of rods of tiled drains are nearly worth- 
less because of not having- been properly lev- 
eled, or not leveled at all. 

y^\ ' SMITH CASTERLINE. 

^ o^ Hartford City, Ind. 



A MANUAL OF 

Leveling and Surveying. 

PART FIRST. 

Leveling and the Level. 

Leveling- is the art of finding- the relative 
position of points, with reference to their dis- 
tance from the center of the earth. 

The difference of level of any two or more 
points, is the difference of their distance from 
the center of the earth. The operations per- 
formed in finding- this difference is called lev- 
eling*. 

The instruments used in leveling- are the 
level and leveling- staff. An eng-ineer's level 
is provided with a fine telescope, with which 
fig-ures, one-half inch in leng-th, can be read 
a distance of thirty and forty rods. The qual- 
ity and power of the telescope adds very much 
to the cost, which, for first-class levels, is 
about $110. The leveling-, however, is done 
with a little bubble, entirely similar to that 
of a common level; the chief advantag-e being- 
the telescope. 

A carpenter's square hung- on edg-e and the 
vertical blade plumbed will bring- the other 
level. Other appliances mig-ht be sug-g-ested, 
but for this work we have adopted the com- 
mon spirit level; such as are used by masons 
and carpenters. It is both simple and cheap, 
and will answer well the ])urp()se. The most 
convenient way of using- it will be on atri])od. 



(4) 
TRIPOD NO. 1. 

This can be easil}^ made as follows: Take 
a block of wood 4 inches long- and cut it in 
shape of a triangle, each side of which should 
measure 6 inches. Cut on one end a round 
tenon, 1 inch in diameter and 2 inj:hes long*. 
Then attach to the other end of the block, 
three leg's 5 feet long*, by means of hing-es. 
The lower end of the leg's must be sharpened 
to stick in the g*round. Trim off the corners 
of the triang-ular block, and the tripod will be 
finished. 

To fit the level for this tripod: Take a 
piece of hard wood 2 by 2 inches, the leng-th 
of the level; and at a point equally distant 
from each end, bore an inch hole throug'h, 
smooth and true, at rig-ht-ang-le to the sides. 
Then, wnth a 5-16 bit, bore another hole 
throug'h from the same side, about 3 inches 
from one end. This is for a leveling'-screw\ 
Then, from the same side and between this 
hole and the end of the stick, with a % inch 
bit bore two holes throug'h, lyz inches apart, 
and cut out the wood between them. This is 
for a clamp screw. Now lay the stick with 
the holes perpendicular and place the level on. 
In this position the two are to be attached by 
a hing-e, at the opposite end from the small 
holes. Place the hing'e open on the two ends, 
using' a hing'e that will allow a space between, 
of at leeist half an inch. A table-hing'e will, 
perhaps be the best. 

The leveling-screw is to be 4>^ inches long', 
having a thread cut nearh^ its entire leng'th. 



(5) 

On one end is to be a round head, 1){ inches 
in diameter and half an inch thick. This 
screw must fit the hole tig-ht enoug*h to cut a 
thread in the wood. Or better, a square tap 
let in the wood at the upper end of the hole. 



g 

^ 
^ 




The chimp screw is to be 3 inches loni;*, 
with a thread cut on one end and a T, one 



(6) 

inch long- made on the other. This is to be 
put throug-h the long- hole and screwed into 
the bottom of the level. Its use is to keep the 
level and its base tog^ether when being- carried. 
To clamp; turn the "T" across the hole and 
tig-hten by the leveling--screw. 

THE SIGHTS. ^ 

The level should be provided with sig-hts. 
which may be done by tacking- to each end a 
thin piece of wood or tin, letting- one edg-e of 
each come ^ of an inch above the surface of 
the level. The insides should be painted black 
and the outsides white. 

TO SET UP THE LEVEE- 

Spread out the leg-s of the tripod and crowd 
them into the g-round. Place the level on, 
unclamp it, and by the leveling--screw, bring- 
the bottom of the level parallel with the base. 
Now bring- the bubble to the center, or nearly 
so, by chang-ing- the position of the tripod legs 
in the g-round. Then turn the level on its 
spindle one-fourth around, and bring- the bub- 
ble to the center ag-ain as before, by forcing- 
the leg's into the g-round. Then turn the level 
ag-ain in the first direction and if the bubble 
is much out, repeat the operation until it will 
remain in the center, or nearly so, with the 
level turned in any direction. Then after di- 
recting- the sig-hts toward the staff, bring- the 
bubble to the center and keep it there b}' the 
levelintr-screw. 



(7) 

, Remark.— It is not expected of this level that the 
bubble will remain in the center during- any part of 
a revolution of the level, btit it should approach to 
that point as near as possible. It is expected the lev- 
eling- up done by the tripod to be done hastily and 
approximateh^; but the correct leveling- is to be done 
by the leveling-screw after the sig-hts are turned in 
the required direction. The first process may be ob- 
viated by using- tripod No. 2. 

TO ADJUST THE BUBBLE. 

Spirit levels that are adjustable have a screw 
b}' which one end of the tube containing- the 
bubble-vial may be raised or lowered. The 
bubble is adjusted to the bottom of the level 
when made; but for our purpose it must be ad- 
justed to the sights. If the sights are exact- 
ly the same hight from the bottom they will, 
very likely, be correct. This may be ascer- 
tained as described after the following- prepa- 
ration. 

Take a board about ten feet long- and drive 
a larg-e wire nail through the middle, near 
one end. Then drive the nail into a post or 
corner of a building, about three feet from the 
ground; and let the other end of the board 
rest on something solid, with its lower edge 
about level. Now tack on two pieces of tin, the 
lengh of the level apart; letting one edge 
come half an inch below the lower edge of 
the board. 

We are now ready to make the adjustment. 
Hold the sights up against the edges of the 
tin, and let the end of the board be rair.cil or 
lowered until the bubble will stand in the cen- 
ter. Then with the sights held against the 
tin, j^jfive the bottom of the level a swin^'iriiif 



,(8) 

motion of about one inch and, while moving- 
it slowly to and from you, notice if the bubble 
runs toward either end; if so, the points in 
contact with the tin are not parallel with the 
bubble-tube. Shift the sig'hts a little on the 
edg-es of the tin, and repeat the operation un- 
til no change in the position of the bubble is 
seen. Then mark the points on both the tin 
and sights where they come in contact; which 
is to insure the same position upon reversing. 
The bubble may not now stand in the center, 
if not, bring it back by the board as before. 
Then reverse the ends of the level, and if the 
bubble runs to the center, the adjustment is 
correct; if not, one-half of the adjustment is 
made by the adjusting-screw, and the other 
half by raising or lowering the end of the 
board. 

Suppose that, upon reversing, the bubble 
runs toward the moveable end of the board, 
you will bring it back half way by lowering 
that end of the bubble-tube, or raising the 
other; and the other half by lowering the end 
of the board. The whole operation should be 
repeated until the adjustment is perfect. 

If the edges of the tin were level, to begin 
with, the bubble could be adjusted in much 
less time. This may be done after the side 
adjustment is made, as follows: Bring the 
bubble to the center by the board; then meas- 
ure exactly the hight of the end of the board 
from some point below. Then reverse the lev- 
el and again bring the bubble to the center 
and again measure the hight of the board 



(9) 

from the same point. Add the two measure- 
ments tog-ether and divide by 2; which will 
g-ive the hig-ht that the board must be, to 
bring- the edg-es of the tin level. 

THE I.KVEI.ING STAFF. 

This should be made of a straig-ht strip of 
wood I by 1>^ inches, and not less than 10 
feet long*. Beg-in at one end and measure ac- 
curately, and mark each foot. Number them 
1, 2, 3, etc. with the larg-est number at the top 
of the staff. Then divide each foot into 10 
equal parts, called tenths. The first one from 
the bottom of the staff, and above each foot 
mark, you will number 1; the next two; and so 
on up to 9. Then divide each tenth into 10 equal 
parts, called hundredths. These need not be 
numbered, but will be read as thoug-h num- 
bered the same as the tenths. The first one 
from the bottom of the staft', and above each 
tenth, will be read 1; the next 2, etc. up to 9. 
Let the foot marks extend across the staff, 
with a larg-e red fig-ure in center. The tenth 
marks extend one-half inch from both edg'es 
of the staff toward the center; with a black 
fig-ure between the ends of the marks. The 
hundredth marks extend from the rig-lit hand 
edg-e of the staff yi of an inch toward the cen- 
ter, with a dot at the end of the fifth or mid- 
dle line. 

Next; place on the staff a sliding" targ-et, to 
be made as follows: Take a piece of wood 2 
by 2 inches, 4 inches long- and cut a ])hice in 
the middle of one side that will iust take in 




H 
9 

9 
-8 

-7- 

6i 

4 
3 

i-2i 

H 
8 




IK^ 



(11) 

the staff the broad way; fasten to this, in front 
of the staff, by small screws, a piece of wood 
5 inches long*, 3 inches wide and a quarter of 
an inch thick. Paint the upper half white and 
the lower half black or red. Where the white 
meets the color will be for the line of sig-ht, 
or point of observation. Now cut out from the 
lower half 1^ inches wide, and up exactly to 
the line of sig"ht. Then bevel from half an 
inch above the notch down to an edg*e. From 
this edg*e the reading's of the staff, when lev- 
eling", are to be taken. The targ-et will need 
a thumb-screw throug*h the back part with 
which to clamp it to the staff. A stick about 
three feet long* will also be needed with which 
to slide the targ-et to points beyond reach of 
the hand. This can be attached by a screw 
to the back part. 

HOW TO READ THK STAFF. 

First; notice what foot the targ-et stands at 
or above. Second; what tenth it stands at or 
above. Third; what hundredth it stands at or 
nearest to. Suppose it standing- above 4 feet, 
and above 7 tenths, and to 5 hundredths; the 
reading- would be 4 feet and 75 hundredths. 
Ag-ain; suppose it standing- above 6 feet and 
to 1 tenth; the reading- would be 6 feet and 10 
hundredths. The staff reading's are expressed 
the same and calculated the same as U, S. 
money; the foot being- answerably to the dol- 
lar; the tenth the dime and the hundredth to 
the cent. 

The above reading's wouhl ])e set down thus: 
4.75 and 6.10. 



.(12) 

The Principles of Leveling. 

Leaving" out the more scientific and theo- 
retical, the practical principles of leveling- 
are few and simple. 

Case 1. — To find the difference of level of 
two points at one setting of the level. 

Sat up the level about an^ equal distance 
from the two points, thoug-h not necessarily 
in line between them. Then let an assistant 
hold the staff upon one of the points and move 
the targ-et up or down until its center line falls 
in line with the sights of the level. Take the 
reading, and then let the staff be held on the 
second point, and note the reading. The diff- 
erence between the two readings will be the 
difference of level. Suppose the first reading 
to be 4 feet and the second 5 feet; it is plain 
that the difference, which is 1 foot, is the diff- 
erence of level. It is also plain that the first 
point is the higher, since a shorter staff was 
required at this point than at the second. 

PRINCIPI.KS OF CASE 1. 

Principle 1. — The difference between the 
readings of the staff will be the difference of 
level of any two or more points at the same 
setting of the level. 

Principle 2, — The longer the staff the lower 
the point, and the shorter the staff the higher 
the point, at the same setting of the level. 

Case 2. — To find the difference of level of 
two points requiring more than one setting 
of the level. 

The points we will designate as point 1 and 
point 2. 



(13) 

Let the staff be held upon point 1 and take 
the reading-; this reading* is called a Back- 
Sig-ht. Then let the staff be held on some 
point as far in the direction of point 2 as the 
targ-et can be distinctly seen, and take the 
reading-; this is called a Fore-Sig-ht. Now pull 
up the level and g-o forward and set it up 
about the same distance beyond the staff, and 
take a second reading- of the staff upon the 
same point where the last reading- was taken; 
this reading- is called a Back-Sig-ht. The staff- 
man will now pass by the level and hold the 
staff on some point about the same distance 
on the other side; the reading* taken at this 
point is called a Fore-Sig-ht. And so continue 
until point 2 is reached; the last reading- or 
that upon point 2 will be a Fore-Sig-ht. The 
difference between the sums of the Back-Sig-hts 
and Fore-Sig-hts will be the difference of level. 
A form for keeping- the levels is g-iven in the 
following- example: 

EXAMPLE. 

Back-Sig-ht. Fore-Sig-ht. 

1 setting-, 8.50 5.25 

2 " 5.10 4.80 

3 *' . 5.00 3.65 

4 '' 4.05 6.70 on point 2. 

22.65 20.40 

20,40 



2.25 
Since point 1 belong-s in the column of 
Back-Sig-hts, and there being- the most staff 
required for the Back-Sigiits, this must be the 
lower of the two points. 



' (14) 
PRINCIPLES OV CASE 2. 

Principle 1. — The difference between the 
sums of the Back-Sig-hts and Pore-Sights will 
be the difference of level. 

Principle 2. — That point which is in the 
column whose sum is the least is the hig'her. 

Suppose point 1 in the above example to be 
in the bottom of a ditch or water course which 
is an outlet for a pond of water some distance 
awav, and point 2 to be in the pond; we find 
the fall to be 2.25 feet. 

EXPLANATION OF SIGNS, ETC. 

Before g'oing- further it will be necessary to 
explain the mathematical sig-ns and terms 
used by eng-ineers. 

This sig-n + plus, means that the numbers 
between which it is placed are to be added 
tog-ether. 

This sig'n — minus, means that the numbers 
between which it is placed are to be subtract- 
ed one from the other. 

This sig-n = equality, placed between two 
numbers mean that they are equal to each 
other. 

This sig-n X multiplied by, denotes that the 
two numbers between which it is placed are 
to be multiplied tog-ether. 

This sig-n -^ placed between two numbers 
means that one is to be divided by the other. 

This sig-n sj placed before a number indi- 
cates that the square root is to be extracted. 

A,Back-Sig-ht is denoted bv B-S. A Fore- 
Sig-ht by F-S. The hig-ht of the level above 



(15) 



the Datum by H. L. The hig-ht of the point 
or station above the Datum by H. The num- 
bers of stations by Sta. Bench Marks by B. M. 

Case 3. — To find the difference of level of 
several points or stations requiring' more than 
one setting* of the level. 

First, an imaginary level plane called the 
Datum Plane, or simply the Datum, is assum- 
ed below the surface of the g-round, and the 
hig-hts above this Datum of all the stations to 
be leveled are found; consequentU^ the differ- 
ence of their levels becomes known. 

The Datum is assumed below the starting 
point far enoug-h to be beneath the lowest sta- 
tion likely to occur on the work; which, for 
local work, is usually 50 or 100 feet. 

We will first g-ive an example, then use it 
to illustrate the three g^eneral principles 
w^hich shall follow. 







EXAMPLE 


;. 






sta. 


F-S. 


H. L. 


B-S. 


H. 




1 




54.20 


4.20 


50.00 




2 


6.32 


54.20 




47.88 




3 


5.15 


54.20 


4.15 


49.05 




4 


2.80 


53.20 




50.40 




5 


3.10 

PKINCI] 


53.20 
PLES OF 


CASE 3. 


50.10 



Prin. 1. The reading- of the staff upon any 
point added to the hig-ht of the point above 
Datum will g-ive the hig-ht of the level above 
the Datum. 

Sta. 1 in the above example is made the 
starting- point and the Datum is assumed 5o 



. (16) 

feet below, which is placed in the column H. 
hence the hig-ht of the point is known. A 
reading- is then taken upon station 1 and set 
in column B-S., which is 4.20. Then 50.00+ 
4.20 = 54.20 is the hig-ht of the level above the 
Datum at this setting*. 

Prin. 2. — The reading- of the staff upon any 
point subtracted from the hig-ht of the level 
above Datum will g-ive the hig-ht of the point 
above Datum. 

With the level setting* in the same position, 
if reading-s are taken upon one or more sta- 
tions in any direction and each subtracted 
from the hig-ht of the level above Datum the 
results will be the hig-hts of the stations above 
Datum. Let the reading- upon station 2 be 
6.32, and upon station 3, 5.15; then, the hig-ht 
of the level being- 54.20, we shall have 

54.20—6.32 = 47.88 the hig-ht of station 2; and 
54.20—5.15 = 49.05 the hig-ht of station 3. 

In the above example the position of the 
level is now supposed to be chang-ed, the hig-ht 
of which must ag-ain be known; this will in- 
volve the first principle. The hig-ht of station 
3 being- known a second reading- is taken upon 
that station and set in the column B-S., which 
is 4.15. Then 49.05+4.15 = 53.20 is the hig-ht 
of the level above Datum at this setting-. Read- 
ing-s are then taken upon stations 4 and 5, and 
by Principle 2 their hig-hts found. 53.20 — 2.80 
= 50.40 is the hig-ht of station 4, and 53.20— 
3.10 = 50.10 is the hig-ht of station 5. 



(17) 

Prin. 3. — The difference of their hig-hts 
above the Datum will be the difference of 
level of an}^ two or more points or stations. 

Since the lig-ures in the column H. show the 
hig-lit of each station above the Datum, b\^ 
simply inspecting- that column we find that 
station 5 is .10 of a foot higher than station 1, 
and that station 4 is the highest and station 2 
the lowest. 

Under the principles of case 3, almost all 
leveling is done; Case 2 ma}^ be brought under 
this case. 

DRAINAGE LEVELING. 

Since the best and quickest way to learn the 
art of leveling is to level, let us make a prac- 
tical application of the foregoing principles 
in leveling for a ditch. 

Take for example a ditch of 16 stations. Be- 
gin at the head and measure and place stakes 
regular distance apart, which is usually 100 
feet, and number them 0, 1, 2, 3, etc., down to 
the outlet. About 4 inches from each stake 
drive a peg, called a hub-ped, down to the 
surface of the ground; from these the levels 
are to be taken. 

Having first provided yourself with a field- 
book in which to take down your levels, a con- 
venient form of which is given on page 23; 
and having secured an assistant you are now 
ready to begin leveling. 

Set up the level near sta. (2), as you will 
not be able to see the targ.^t to set it correctly 
more than 200 feet each wav. Then proceed 
as in Case 3; and write down the results as 
shown in the example of field-notes. The D:i- 



(18) 

turn which is assumed 50 feet below sta. (0) is 
set in column H. A reading- is then taken 
upon sta. (0) and set in column B-S. This 
reading* is added to the Datum, which g-ives 
50.00+3.00 = 53.00 feet for the hig-ht of the 
level above Datum. (Case 3, Prin. 1.) Read- 
ing's are then taken upon sta. 1, 2, 3 and 4, 
which are set in column F-S; and each sub- 
tracted from the H. L., which g-ives the hig-ht 
of each station above Datum. (Case 3, Prin. 2.) 
The level is now removed to between sta.(6 ) 
and (7), and a back-sig-ht taken upon sta. (4). 
This reading- added to the hig-ht of the station 
ofives 50.65+3.60 = 54.25 feet for the hiofht of 
the level above Datum at this setting-. Read- 
ing-s are then taken upon sta. 5, 6, 7 and 8, and 
the hig-ht of each found as before. Proceed 
in like manner with the balance of the sta- 
tions. Observe that at sta, (6) a Bench is es- 
tablished. The reading- of the staff upon the 
Bench is subtracted from the H. L. which 
g-ives (54,25— 2. 53) = 51. 72 for the hig-ht of the 
Bench above Datum. 'Case 3, Prin. 2.) The 
point where a Fore-Sig-lit and Back-Sig-ht is 
taken, is called a turning- point; this is usual- 
ly made upon a station, but not necessarils' so. 
In the example g-iven, after a reading- was ta- 
ken upon sta. [12], because of some obstruct- 
ion between it and sta. [13], the staff was 
held upon some point off to one side and the 
F-S. and B.-S. taken from it. It does not 
matter where this point is, nor how hig-h or 
low; the only object in a Back-Sig-ht being-, 
after the level has been reset, to g-et its hig-ht 
ag-ain above the Datum. 



(19) 
THE GKADE LINE HOW EvSTABLISHED. 

1. Having- first determined the depth of 
cut necessary to be made at the head or sta. 
[0], subtract it from the hig-ht of the station, 
the remainder will be the hig-ht of g-rade of 
that station; which set in the column Grade. 
Also set the hig-ht of the lower end station in 
column Grade. 

In the example let the cut at sta. [0] be 2.35; 
th?n 50.00— 2.35-^47.65 will be the hig-ht of 
grade above datum; and 45.25 the hig-ht of 
the other end, or station 16. Then 

2. F'ind the total fall of the grade line. 

The difference between the hig-hts of the 
two ends in column Grade will be the total 
fall. [Case 3, Prin. 3.] 

In the example, 47.65— 45. 25 --2.40 is the 
total fall. 

3. Find the averag-e fall per station. 

Divide the total fall by the number of sta- 
tions. 

2.40^16~.15 of a foot per station. 

4. Find the hig-ht of the g-rade line above 
datum at each station. 

Beg-inning with sta. [0] the g-rade bight of 
each station is decreased by the averag-e fall 
which gives the hig-ht of the station l)elOw it; 
or, beginning at the other end, the liight is 
increased by the averag-e fal] lor the higlit of 
the next station above it. 



(20) 



Beg-inning- with sta. 16, the hig-ht being- 
45.25, you will proceed as follows: 

45. 25+. 15 = 45. 40 grade of station 15. 
45.40+. 15 = 45.55 " " 14. 

45.55+. 15 = 45. 70 '' " 13 etc. 

Beg-inning* with sta. (0) we will establish 
the grade line of the entire ditch. 

47.65 grade of station 
.15 = 47.50 



47.65- 

47.50- 



J5 = 47 



47.35 — .15 = 47 



20 



47.20— .15 = 47.05 
47.05— .15 = 46.90 
46.90— .15 = 46.75 
46,75— .15 = 46.60 
46.60— .15 = 46.45 
46.45— .15 = 46.30 
46.30— .15 = 46.15 



46.15— 
46.00— 

45.85— 
45.70— 

45.55 — 



46.00 
45.85 
45.70 
.15 = 45.55 
.15 = 45.40 



15 = 
15 = 
15 = 



45.40— .15 = 



0. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 



= 45.25 

CHANGE OF GRADE. 

In long- ditches it frequently occurs that one 
or more chang-es of g-rade is necessary, in or- 
der to avoid too deep cutting- in some places 
and not deep enoug-h in others. The points 
along- the line where chang-es in the g-rade 
should be made can be determined best by 
drawing- a profile of the surface, the method 
of which will be hereafter described. 

Taking- the above for an example, suppose 
that on reaching- sta. (9) the ditch should be 



(21) 

found running' too shallow; to prevent this 
the fall must be inereased, say to .20 of a foot 
])er station. Then, 

46.31) grade of station 9. 

46.30 -.20=46.10 '' '' 10. 

46.10--.2e=45.00 '^ ^' 11. ete. 

If the g-rade is found running- too deep the 
fall per station would have to be deercased. 

TO KIND THE DEPTH OF CUTTING. 

To hnd the depth of cut at each stake it i\\ 
necessary only to subtract the iig*ures in the 
column Grade from those in the column H. 

BENCH MARKS. 

Bench Marks, denoted by B. M., are estab- 
lished at convenient distances apart along' the 
line of work b}^ cutting- a notch on the root of 
a tree, wdien timber is near, or b}^ taking- some 
object as a larg'e stone, corner of a building-, 
or any stationary object on which the staif 
can be held. Their use is to enable an engi- 
neer to retrace a g-rade line either while the 
work is being- done, or years after its comple- 
tion. 

To establish a bench: Take a reading- of 
the staff upon the bench and subtract it Ironi 
the hight of the level above datum; (Case 3. 
Prin. 2.' and mark the object on which the 
bench is made with the letters B. M., follow- 
ed by the number orresponding to that n\^ the 
station to which it is nearest, as B. M. (>. 

To I'lM) Tin: (iiCADi: I.IM<: 1 KO.M A HKNCII .MAKK. 

Take a reading of the staff upon the bencli 
and add it to the hight of the l)ench al)ove 



datum; the sum will be the hig-ht of the level 
ciDove datum.. (Case 3, Prin. 1.) Then the 
difference between the hig*ht of level and 
hig-ht of grade at a g-iven point wall be the 
rending- of the staff when held on the grade at 
that point. (Case 3, Prin. 2.' 

L:^t U3 takj for example the B. M. al sta. 6 
of our example ditch, and find from it the 
5>-rade at sta. 4 and 8; supposing- the read- 
in.g" of the sta.ff upon the bench to be 3.23. 

Example. 
Hight of B. M. above datum 51.72 
Reading- of the staff on B. M. 3.23 
Hig-ht of level above datum 54.95 

Hight of g-rade at sta. 4 47.05 

The required reading- 7.90 

Hight of level above datum 54.95 
Hisrht of trrade at sta. 8 4*6.45 

o o 

The required reading 8.50 

Tiie principles of Case 3 are the principles 
under v/hich street gTades are established. 
Some permanent point is chosen for a bench 
mark from wdiich to begin leveling, and a da- 
tum assumed, usually 100 feet below^ it; then 
levels are taken at street crossing's, alleys and 
other bench marks, all of which are referred 
to the same datum. The method of finding 
the grade line at anv point is the same as that 
given above. The engineer after he has fin- 
idied leveling and made out the grade, files 
his notes of such grade in the office of the 
town clerk who places the same upon record, 
and all street improvements thereafter are 
made conformable to said or^ade. 






ICXAMPLK 01< KIHI.D XOTKS. 



vSl-< 



I-S. 


H.L. 




53.00 


2.50 


53,o;) i 


2.10 


53. OJ ; 


1.50 


53.00 ; 


2.35 


5:^.00 : 


2.80 


54.25 ; 


3.00 


54.25 : 


2.5^ 


54.25 ^ 


.-^.2:) 


54.25 : 


5.50 1 


54.25 I 



B S 



3.00 



.CO 



10 

12! 
Lirnl 
13, 
14 
15 
16 



4.50 
4.40 
4.75 
4.90 
5.00 
4.15 
5.00 
5.50 
6.25 



^_^ 
52. 
52 
52. 
51. 
51 
51. 
51. 



.50 





1 


1 


; R'~ 


H. 


|Grad( 


^i Cut. 


iiiiarl, 








1 


J, 


50.00 


47.65 


1 2.35 


] 


50.50 


47.50 


! 3.00 




50.90 


47.35 


3.55 




51.50 


47.23 


i 4.:0 


i 


50.65 


47.05 


; 3.60 


i 


51.45 


46.90 


4.55 


1 


51.25 


46.75 


; 4.50 


1 Oal-: 


51.72 


46.75 




'2 rd. n 


51.05 


46.60 


1 <,45 


e. of 6 


48.75 


46.45 


' 2.30 




47.^0 


46..-0 


1.20 




47.60 


46.15 


1.45 




47.25 


46.00 


1.25 




47.10 


45.85 


1.25 




47.00 








47.35 


45.70 


1.65 




46.50 


45.55 


.95 




46.00 


45.40 


.60 




45.25 


45.25 


0.00 





DRA-tV'ING THE PKOFILK. 

After any work has been leveled the surface 
<>t the ground and grade line may be repre- 
sented upon paper in the following- manner- 

rake ruled paper and draw a line crossin"- 
the ruled lines, and let it represent the datum 
line, and let the ruled lines represent the sta- 
tions. Also ict one inch rep^resent a e, rtain 
numlK-r ol levt fr,r the vertical scah-. 'Ph. „ {-;■ 
the hig-ht ol each station in the column F is 
measured by the same scale, and their distan- 
ces set olf lr<un tiic datum on the perpc ndice- 
lar rulmg-s, a lin,' drawn throug-h those poin<-. 
will represent th.- surface of the ground Thv 



, (24) 

grade may also be represented b}^ drawing* a 
line throug-h two points measured b}' the same 
scale. 

The instruments emplo3'ed in drawing- pro- 
iiies are dividers or compasses, drawing- pen, 
ruler and a diagonal scale having one inch 
divided into 100 equal parts. 

Suppose that you v/ished-to draw a profile 
of the foreg'oing* ditch to a scale of 5 feet to an 
inch. Draw the da^tum line near one edg-e of 
the paper and place below it on the ruled lines 
the number of the stations from to 16. 
Station 16 being* the lowest, subtract its 
hig-ht from the hig-ht of each of the other sta- 
tions; then the distances to be set off on the 
perpendicular ruling-s will be found by divid- 
ing- the hig'hts thus found by 5 feet. The 
hig-ht of sta. 0, 50.00—45.25^4.75 and 4.75 
-^5--.95 of an inch. Now spread the dividers 
so that when applied to the scale of equal 
parts they will embrace 95 parts or hundredths 
of an inch. Place one arm of dividers on the 
datum at sta. and the other above on the 
ruled line, and mark the point by a small dot. 

The hig-ht of sta. 1, 50.50—45.25 = 5.25, 
and 5.25^5 — 1.05. Take one inch and five 
hundredths between the points of the dividers 
and with one arm on the datum at sta. 1 , 
dot the point above to where the other reach- 
es. The hig-ht of sta. 2, 50.90—45.25 = 5.65 
-f-5 — 1.13 inches. Measure and mark this dis- 
tance above the datum on sta. 2, as above. 

In like manner measure and mark the hig-ht 
of each station; then a line drawn, off hand, 
throug-h all of those points will represent the 



surface of the ^y-round. The grade line may 
now be drawn under the surface line. The 
i^-rade higiit at sta. 0, 47.65— 45. 25 ^=2.^40 -f- 5 
-.48; measure 48 hundredths of an inch from 
the datum on sta. 0, and with a ruler laid at 
sta. 16, draw^ a line from to 16. 

I'he points where cheing-es in the grade 
should be meide, if an}^ should be necessary, 
can be determined by stretching' a fine black 
thread under the surface line. 

Paper called profile paper is made for the 
<Lb()ve purpose, and is ruled in such a manner 
that no drawing instruments except a drawing 
]>en is needed in drawing' profiles. 

GKADE STAKES AND THEIR USE. 

The use of grade stakes, when once under- 
stood, will not be abandoned by any ditcher. 

By their use no water for g-rading* is needed 
and each foot may be tiled, if need be, before 
entering- upon the next. The stakes may be 
prepared and arranged for use, all wnthin a 
few minutes, as follows: Take three small 
stakes and split (me end of each, and place in 
each split a thin piece of white wood about 5 
inches long- by 1 inch wide, so as to form a 
•'T,'' and sharpen the other end to stick in the 
ground. The length of one should be5'_' feet; 
the length of the other two will vary, (me will 
be longer and the other shorter. We are now 
ready to arrange them for use; and for this 
pur])ose let us use our exami)le ditch. 

1. Place the 5' J foot stake ])er])endiciilar 
at sta. 1(), with the **T" five feet above tlir 



(26) 

2. — Place the shorter stake at sta. 15, so 
that the ''T" will be ^ve feet above the g-rade 
line. To do this subtract the depth of cut 
from live feet; the remainder will be the hig-ht 
of the '"T" above the hub-peg-. The cut at 
sta. 15 is .60; then 5.00— .60^4.43 will be the 
required hig-ht. 

3. — Place the third stake about 100 feet 
below sta. 16 and rang-e the *^T'' horizont- 
ally \yith the other two. 

Now having the g-rade stakes set parallel 
v>uth the grade line, five feet above it; and 
having provided yourself with a 5 foot meas- 
uring stick, you are read}^ to begin work. As 
you dig- from sta. 16 toward 15 the depth ma}' 
be tested at any time by holding* the measure 
perpendicular on the bottom; if cut the proper 
depth the upper end of the measure will range 
with the tops of the grade stakes below you. 

When the digging is completed up to sta. 15 
the stakes must be reset. Take up the stake 
at sta. 15 and set it at 14; the cut at this point 
being .95 the hight of the '^T'' above the hub- 
peg 'will be (5.00— .95=) 4.05 feet. Then 
bring the stake from sta. 16 and place it at 
15, with the ''T'' 5 feet above the grade line. 

Then set the third stake atsla. 16 and range 
it with the other two as before. 

When the depth of cut at an}' point is more 
than 5 feet, cut out until less than 5 feet 
before setting the g-racle stakes. 

If the grade styke to be used ahead was 
provided with a sliding targ-et it would save 
the trouble of having' frequently to make new 



(27) 

ones. The reason why is phiin; at sta. 15 the 
hi<4'hL required abov^e the hub-peg" is 4.40, 
while at sta. f) it will ])e only (5.00 -4.50" ) 
.50 of a foot. 

THK CKADIC STAKES AS A LKVKL. 

If two <>Tade stakes are set up say 50 feet 
apart in a pool of water with their T's exactly 
the same hig"ht aboye its surface, a straig-ht 
line connecting- them or extended beyond will 
be a line of appcirent ley el, and will answer 
for leyeling- ditches not more than one mile in 
leng-th; but if longer than one mile the curva- 
ture of the earth should be taken into consid- 
eration. 

The principles for this method of leyeling- 
are the same in all respects as those cilread}' 
g-iven, except that no l)ack-sig-hts are taken. 

A datum is assumed and the liig*ht of the 
level line above the datum is kept the same as 
when using- a level. 

To illustrate, let us employ the g-rade stakes 
in. leveling- our example ditch. First let there 
])e a shallow trench dug" 40 or 50 leet long", 
some where between sta. and 1 or 1 and 2, 
and allow it to fill with water or until the 
bottom, at least is covered; and when not in 
motion place in it two grade stakes as above 
slated. Then let the staff ])e held upon sta. 
and the target broug-ht in range with the tops 
<'l the stakes and take the reading, which we 
will suppose to be 5.00 feet. Then, the datum 
hight of sta being" 50.00 I'cct. we shall have 
I 50.00 -f-5. 00-55. 00 for the hight of the level 
line above datum; which enter in column H L. 



(23} 

Now extend this level line b}^ setting- more 
stakes about one hundred feet apart and rang- 
ing- them horizontally with those in the water 
and with each other until the end of the ditch 
is reached, or as far as the rise or fail of the 
ground will admit; taking a reading of the 
staff upon each station as you go, which you 
will place in column F-S. 

Suppose that at some point, as near sta/). 
a fall of the ground makes it necessar}^ to 
lower the level line say 2 feet. Set the target 
at 2 feet on the staff, then let it be held on a 
grade stake about one hundred feet from the 
last stake set or near sta. 10, and force the 
stake into the ground until the target comes 
in range with the two last set; then the one 
on which the staff is being held will be 2 feet 
below. In like manner set another near sta. 9. 

Two feet must now be subtractrd from the 
datum hight, leaving it 53.00 feet; then you 
vvill proceed as frcm the beginning. The 
level line may also be raised or lowered by 
setting two stakes an equal distance abov^ or 
below two already set. The datum hight 
must be changed accordingly. 

The accuracy of work done by this method 
of leveling depends upon careful measuring 
and setting of the grade stakes, as the level 
to begin with is a good one. 

A further explanation of this method of 
leveling is deemed unnecessary, as it will be 
understood on becoming familiar with the 
foregoing principles. 



(29) 



WIDTH OF DITCHEvS HOW COiMPUTlvD- 

Ditches arc of two kinds, open and covered. 
The width at top of bank of an open ditch vr> 
g'overned by its depth, sh>pe of banks and 
width on bottom. The banks should have a 
uniform sh)pe of not less than one foot hori- 
zontal to each foot perpendicular. 

RuLK. — Multiph^ the depth of cut b}^ double 
the slope of one bank and add the bottom 
width. 

For example let us compute the width at 
sta. and 1 of our example ditch; supposing- 
the bottom width to be 2 feet, and slope of 
banks to be 1 to 1. 
Depth of cut at sta. 
Double the slope of one bank 



9 



Bottom width 
Width at top of bank 
the depth 



4.70 
2AA) 
6.70 



At sta. 1 the depth of cut 3.00x2 
2.00-^8.00 feet at top of bank. 

]:XCA\'ATI0N HOW COMPUTED. 

^Phe unit of measure for measuring* excava- 
tion in cutting ditches, road making, etc. is 
the cubic yard. 

A cube is a ligure, having* six e(|ual sides, 
which are scjuares. .V l)ox measuring- three 
feet scjuare inside will hold a cubic yard. 

TAIUJ-:. 

172S cubic inches make 1 cubic foot ( cu. ft ». 

27 cubic feet ** 1 cubic yard • cu. yd i. 

In ordur to find the cubical contents of a 

solid it nllI^t lirst be scjuared, if it is not, then 



. (30) 

apply the following-: 

Rule. — Multiply the leng-th, breadth and 
thickness together and divide by the unit of 
measure. 

Now let us find the number of cubic yards 
in sections 1 and 2 of our example ditch; sup- 
posing- the slope of banks to be 1 to 1. 

1. Find the averag-e depth of the section. 
Depth of cut at sta. 2.35 

'' 1 3.00 

2 ) 5.35^ 



Averag*e depth 2.675 

2. Find the top width. 

Average depth 2.675 

Double the slope of one bank 2 

5.350 
Bottom width 2.00 

Average width at top of bank 7.35 

3. Square the section. 

Width at top of bank 7.35 

Width on bottom 2.00 

2~) 9.35^ 



Average width 4.675 

4. Appl}^ the above rule. 



Average depth 

Average width 


4.675 
2.675 




23375 
32725 
2 8050 
9 350 


Cu. ft. per foot 
Length of section 

27 


12.505625 

100 
) 1250.5625 ( 46.31 cu.vds. 



(31) 

When the slope of banks is 1 to 1, add the 
bottom width to the averag-e depth ;which will 
give the averag'e width or square of the sec- 
tion. In the above case, let the bottom wndth 
be added to the averag-e depth, and we shall 
have 2.675+2.00 — 4,675; the same result as at 
3. Therefore the operations at 2 and 3 are 
unnecessary except when the slope of banks 
is other than 1 to 1. 

(Computation of section 2. 
Depth of cut at sta. 1 3.00 

'' 2 _3_^55 

2T^^55 
Averag-e depth 3.275 

Width on bottom 2.00 

Average width or square 5.275 

3.275 
26375" 
36925 
1.0550 
15.825 
Cu. ft. per foot 17.275625 

Length of the section 100 

27. ) 1727.5()25 ( ()3.0S cu. ydr. 

CxICNKKAL KrLl\ 

For computing- the contents of a section: 

1. Add tog-ether the depth of cut at each 
end of the section and divide the sum by 2. 
which will g-ive the averag'e depth. 

2. Multii)ly the average depth l)y (loubl*.- 
the sl()])e of one l)ank and add the bottom 
width, which will gi\'e the axeragt.' widtli at 
to]) of banl<. 



2. Add the top and bottom widths tog-ether 
and divide b}' 2, which wnll g-ive the av^erage 
width or square of the section. 

4. Multiply the average wndth by the aver- 
age depth and this last by the length of the 
section, w^hich will give the contents m cubic 
feet. 

5. Divide by 27 for the cubic j^ards. 

FOR DITCHES THAT ARE TO BE TILED. 

No definite rule can be given for calculating' 
the wndth. The bottom should be just wide 
enough to receive the tile, w^iile the top must 
be W'ide enough to allows free use of the body 
in casting' out the dirt. An averag*e width of 
two feet will, ordinarily, be a fair estimate. 

RULE. 

1. Add together the depth of cut at each 
end of the section and divide the sum b}^ 2, 
which will g-ive the averag-e depth. 

2. Multiply the averag-e depth by the aver- 
age with, 2 feet, and this result by the leng-th 
of the section, and divide by 27. 

THE WORK OF EXCAVATIXCx HOW ESTIMATED. 

This will depend upon at least two con- 
ditions. First, the nature of the g-round. 
Second, the distance that the dirt will have to 
be removed. The nature of the ground m 
many phices varies all the w^ay from muck to 
hardpan. A common spade can be put down 
its length into muck, soil or soft cla}- by one 
or two exertions, while in hard cla}^ six or 
eight exertions will be required: and hardpan 
will require a pick and shovel. 



133) 



Now, suppose the above varieties of earth 
are to be cast from a ditch not to exceed live 
feet in depth nor more than twelve feet wide. 

An ordinary ditcher, in ten hours, will cast 
from this ditch 20 cubic yards of muck or soil, 
or 15 cubic yards of soft cla}' or 10 cubic yards 
of hard clay, or from 6 to 8 cubic yards of 
hardpan. If the price allowed for 10 hours 
labor is SI. 50, then will 

SI. 50-^ 20 cu. yds. = 7y2C. for muck and soil. 
1.50^15 '' ^ '' ^^lOcts. " soft clay. 
1.50^10 '' '' " 15 '' '' hard clay.' 
1.50-^7 '' " ^'21 3-7 " heirdpan. 

In the above estimate no allowance is made 
for adhesive clay, stumps, roots, etc. If such 
occur due allowance should be made. 




(34) 



PART SECDND. 

Hints on Land Surveying^. 

In connection with the foreg-oing* work on 
leveling-, a few suggestions upon the subject 
of land surveying- will not be considered out 
of place, as the two g-o tog-ether. 

The principal instruments used in surve}'- 
ing- are the transit or compass, and chain. 

The compass is strictly a mag-netic instru- 
ment, while the transit is not. The transit 
is provided with a telescope, while the com- 
pass may or may not be. The price of trans- 
its rang-e from $130 to S200, and compasses 
from S30 to S75. 

A very g-ood substitute for the compass can 
be made by a mechanic, with which lines can 
be surveyed and rig'ht-ang-les set off with as 
much precision as wnth a real compass, as fol- 
lows: 

THE COMPASS. 

Make two wheels of well seasoned wood, 
16 inches in diameter and half an inch thick. 
Put them tog-ether with screws, their grain 
crossing each other. Then make another 
wheel 3 inches in diameter and 1 inch thick, 
and fasten it in the center of the other wheel 



135) 

Avith nails or screws. This will be the under 
side of the compass wheel. Draw two lines 
on the upper side, crossing- the diameter ex- 
actly at rig-ht-ang-le to each other. At the 
intersection of these lines bore an inch hole 
throu"-h, smooth and true. Next take four 




thin pieces of wood. 1 inch wide and S inches 
long-, and make a slit l-.^2 of an inch wide 
throug-h the middle of each, to within one inch 

I of each end. These being- for the sights tlu'v 
must be fastened to the (.'d^^^- of the wheel or 

I let in their thickness, so that their slits will 



' (36) 

be parallel to the hole throug'h the center and 
coincide with the lines drawn across the wheel. 
This may be done in the following- manner: 
I-^^j the wheel on something- solid, with the 
hole unobstructed, and suspend a fine line 
throug-h the hole, with the bob in water to 
keep it from swinging-; then fasten the wheel 
in such a position that ihe plumb-line will 
center the hole clear throug-h. With the 
wheel in this position the sig-hts, when made 
fast to it, must all be parallel to the plumb- 
line and each pair exactl^^ in range with it. 

If a hole }i of an inch is bored throug-h near 
the upper end and one in the middle of each 
slit, it will aid very much in catching- a view 
of the flag*-staff or other object throug'h them. 

SPIRIT LEVELS HOW ATTACHED. 

The sights of the compass when in use must 
be perpendicular; for this purpose two spirit 
levels will be required. Pocket levels, which 
will be very good for the purpose, can be 
obtained from almost any hardware store at a 
cost of about 15 cents. They are made with' 
a clamp-screw on one side for the purpose of 
clamping- them to the edg-e of a carpenter's 
square; and in order that they may be attached 
to this compass, an edg-e must be raised on 
which to fasten them. Take a piece of heavy 
tin 2>2 by 1^2 inches, and bend it lengthwise 
in the middle, to a right-angle. Make two 
holes through one side for screws, and fasten 
it on the wheel about three inches from a 
sig-lit, so the line drawn across the wheel will 
divide it in the center; the other side will then 



(?>7) 



1)0 vertical, on the edg*e of which the level 
mav be clamped as en a square. In like 
manner place another across the line between 
the other pair of sig*hts. 

TO ADJUST THK LKVKLS. 

Place the compass on the tripod and suspend 
a line line near b3\ After bring-ing- the com- 
pass to a horizontal position, direct a pair of 
sig'hts to the plumb-line and bring- the slits 
of the sig-hts parallel to it. With the compass 
in this position the bubble should stand in 
the center, but if it does not the edg-e of the 
tin at that end to which the bubble runs must 
be filed down until it will stand in the center, 
l^hen turn the other pair of sig-hts to the 
plumb-line and in like manner adjust the other 
level. 

TKIPOD NO. 2. 

A tripod having a ball and socket joint, on 
which the compass and level may both be 
used, can be made as follows: Take a block 
of well seasoned wood and make a wheel (> 
inches in diameter, by 2 '4 inches thick end- 
wise of the wood. Bore a 2 inch hole throug'h 
the center and rout out one end, or what 
would be ])etter have it turned out on a lathe, 
large enoug'h and in shapr to receive a ball 
.Vj inches in diameter, one-haif its diameter; 
so the hall will be just a loose fit. This torms 
the lower halt oi tlu' socket. To the lower 
L'dij^e of this sock<.'t is to be attached three leg's 
similar to those for tripod No 1. Matteii 
three places equally distant apart just *.nough 
to receive the hinges. The U])])er end of the 



(38) 



leg's will have to be beveled a little on the 
side opposite the hinges, or else they will come 
in contact with the under side of the socket 
and will not close. Next cut from a seasoned 
board, 1^ inches thick, another 6 inch wheel 




Fi^. 2 veprespwfs ot}e-li(ilf of Fig. 1. 
a, s])iiidJe; h, flange; c, bnJJ ; (J , loop; e, it])])rr 
socket; f, lower soeket. 

and turn or rout out a place in the center that 
will take in the 3^2 inch ball, one-half its 
diameter. The hole through the upper side 
will be nearly 2>2 inches. This will form the 
upper socket. 



(39) 

Having- selected from a croquet set, a hard 
wood ball of the above dimensions, place it in 
the socket between the two wheels. Then, 
with a l4 inch bit, bore three holes throug"h 
both wheels about half an inch from the 
outer edg'e, and at points half way between 
the hing-es. Put bolts throug*h these holes 
from the under side, with washer and thumb- 
tap on the upper side. Then take the ball 
out and line the socket with thin, but g-ood 
leather. The ball must have an inch hole 
bored throug*h the center, which should be 
endwise of the wood. The points where the 
iKill is finished in turning* marks the axis or 
center; throug-h this axis the hole should be 
bored. This is to receive the spindle which 
is to hold the compass wheel. 

The spindle can be made of wood, but better 
made of tin. It must be 1 inch in diameter 
and 5 inches long-. A flang-e 2/j inches in 
diameter, made of heavy tin, is to be soldered 
to the middle of the spindle, at rig-ht-ang-le to 
it. On this flang-e the compass wheel i^s to 
rest. One end of the spindle is to be inserted 
into the ball 1 r>-S inches or just to the center, 
and fastened in with g-lue. Tliis end is to be 
capped and a small hole jninclied throug-h the 
center of the cap from the inside. Throug'h 
this hole a string" is to be inserted and a knot 
tied on the end that will not pull throug-h the 
hole; it should ])e about four inches long-, with 
a loop on the lower end from which to susi>end 
a pluni])-line. A small hole should be made 
tliroug-li the U|)])er end ol" the >]»iii(l]e and a 



(43) 

spring--piii put tliroug-h to keep the compass 
from falling- off while being- carried. The 
ball should have about half an inch sawed off 
fr.)m its lower part and the hole flared, so that 
th • plumb-line will have plenty of room. Be- 
fore putting- the parts of the tripod tog-ether 
tli: Hocket should be well rubbed with cold 
tallow. 

In order that this compass ma}^ work well 
and true, it must be made exact in all its parts. 
The hole throug-h the center of the wheel must 
be a rig-ht-ang-le to its under surface, and must 
fit the spind.le so exact that there can be but 
on: motion. The sig-hts must be parallel to 
the hole throug-h the center, and one pair 
exactly at rig-ht-ang-le to the other. The 
socket must be made in shape to fit the surface 
of the ball. The ball must be true, and the 
hole bored exactly through its center. The 
spindle must be perpendicular to the horizon- 
teil axis of the ball; and must be round. All 
of which can be done by an ordinary mechanic 
with the proper tools. 

TO SET UP THE COMPASS. 

Set up the tripod over the corner or point. 
Pat the plum-string throug-h the loop and tie 
it around the string- below. Then force the 
legs in the g-round so as to bring- the point of 
the plumb-bob directly over the corner. Then, 
after turning the sig*hts in the required direc- 
tion, bring- the bubbles to the center. Should 
the ball work too tight or too loose, reg"ulate 
it by the thumb-taps. 



(-11) 



THK CHAIN. 

The chain used by surveyors is four rods or 
sixty-six feet in leng^th, and consists of 100 
links. This chain, once considered infallibh^, 
is now almost "a thing* of the peist.*" The 
steel tape, which is much lig"hter and a more 
accurate measure, is rapidl}^ superseding- it. 
They are of various leng-ths and g-raduations; 
for surve^'ors use they are made 66 feet long- 
and g-raduated to links, thoug-h tapes which 
are only two rods or 33 feet long- are often 
used. 

A very g-ood measuring- line can be made of 

tin, as follows: Get a tinner to cut strips of 

tin 3/^ of an inch wide, and solder the ends 

tog'ether until 34 feet is made. Attach to the 

ends suitable handles, made of No. 9 wire, so 

they will turn in the end of the line. Take a 

T)iece of heavy tin 2 inches long- by half an 

inch wide and solder it leng-thwise on the line 

next one handle, with one edg-e even with the 

|edg-e of the line. The shoulder formed by the 

Iprojecture will be the rear end of the line 

mroper- the points from which measurements 

begin. Measure from this point exactly 33 

I feet and solder on a similar piece of tin. with 

lone end at the 33 feet and the other in the 

[direction of the rear end; and let this shoulder 

Ibe at the same edg-*.' of tlu* line as the other. 

iTrim off both rearward shoulders. 

(iraduate the line to suit your own conven- 

lience. When not in use coil it u]) and tie it. 

This is not nierclv a toy line, but it ])os- 

'ssus real merit. 1'he author had one made 



50.8 feet long- for a special job. expecting- when 
done to throw the line away, should it last 
that long-. After two years use, upon testing 
it by a Chesterman steel tape, althoug-h some- 
what kink}' was found the proper leng-th. 

AIARKIXG PINS. 

These can also be made by a tinner. Xo. 
9 wire will answer the purpose. They should 
be 14 inches long-, sharpened at one end and a 
small ring- bent on the other. Eleven pins 
constitute a set. Short strips of red flannel 
tied in the ring-s will render them more con- 
spicuous in tall grass or weeds. An open ring 
made of wire will be most convenient on which 
to carry them. 

Now. having all the necessary instruments 
for running lines, the next in order will be to 
learn to use them. So let us begin with the 
chain. 

IXSTRUCTIOXS ox CHAINING. 

In the operations of surveying, as much 
depends on correct chaining as upon any other 
part of the work. In fact, more skill is re- 
quired to do correct chaining than to manipu- 
late the instrument. 

Let us proceed in regular order to measure 
between two points which are visible from 
each other. Place a flag- staff at the opposite 
end from which you wish, to begin. Uncoil 
the line and stretch it out with the front end 
in the direction of the flag-staff. Let the rear 
chainman, called the follower, place the 
shoulder of the line against a marking pin put 
down at the starting point. The front chain- 



(43) 

man, called the leader, will now take the re- 
maining* ten pins, and after pulling- the line 
taut, stick one down perpendicular ag^ainst 
the other shoulder. The line will now be 
carried forward another leng-th and the rear 
shoulder placed ag-ainst the pin just put down, 
while the leader sticks another pin. The fol- 
lower will see that the leader places the pins 
in line with the point to which they are run- 
ning-. When the leader has put down his last 
pin, he will receive from the follower the ten 
which he has taken up. The point where the 
leader runs out of pins is called an ''out" and 
a stake called an "out stake" is usually driven 
at this point and the meeisurement continued 
as from the beg-inning-. If the leng-th of the 
chain or line being- used is 33 feet, the dis- 
tance between the ''out stakes'- will be twenty 
rods- five chains. This line being- measured 
for practice, should be measured back ag-ain 
and the results compared. 

In order to do correct chaining*, the follow- 
ing sug-g-estions should be observed: 

Before starting- to measure aline, the leader 
should see that he has the required number of 
])ins. He should j/ull the chain always with 
the same tention. After putting- down a pin 
he should stand erect and see that the pin 
does, then call out ''struck.' When the rear 
end of the chain comes U]) to the ])in, tlic fol- 
lower should call out "slick." He should 
g'uide the leader, and see thai lie ])uls the ])ins 
down in line with the ])oint to which thev are 
runnini'-. He should not allow the ])in to be 



(44) 

pulled over by the leader nor pull it up him- 
self until the leader calls out ''stuck." He 
should count the pins at each "out" to see that 
none are missing-. Chainmen should make 
their backs bend, and not cut a ''new moon" 
with the chain while sticking the marking- 
pins. The chain should be held level no 
matter how irregular the ground. In chain- 
ing up or down hills,-' use a plumb-line or 
straight-edge in locating the points on the 
i^Tound. When too steep for the whole length 
of the chain, use such equal parts of it at a 
tim:^ as can be reached, the leader being care- 
ful to leave a pin onl}^ for each entire length. 
Each chainman should be careful during a 
halt, or any interruption, to keep possession 
of his own pins and not allow them to get 
mixed, as they do the counting. 

PRACTICE WITH THE COMPASS. 

This compass, more properl}' called a cross, 
having no magnetic needle or graduated circle, 
is adapted only to rectanguluar survej'ing*, as 
no ang'le less than ninety degrees can be taken 
with it. Though much surveying is done 
without using the needle, even with needle 
instruments; and aside from a telescope com- 
pass this one is as well adapted to running 
lines as a common compass. 

Case 1. Let it be required to run a line 
which shall be a right-angle to a given line 
from a given point on that line. 

Set up the compass at the given point, level 
it and turn one pair of sights on the given 
line; the other pair will then be in the direc- 



(45) 

tion of the required line. Let a tlag*-staff now 
be set up on the line as far as it can be dis- 
tinctly seen throug'h the sights, and another 
a short distance in the opposite direction, 
called a back-stake. Now take up the com- 
pass and g*o forward and set it at the point 
where the fiag'-staff stood, and after leveling- 
it direct a pair of sig-hts to the back-stake; 
when they will ag'ain be on the line. Thus 
the line ma^^ be extended at pleasure. When 
the line is being* measured, the ''out stakes' 
will serve for back-stakes; they should be four 
or five feet above the g-round and their tops 
hewn so that they may be easily seen. 

Case 2. Let it be required to run a line on 
which there are obstructions, such as a larg-e 
tree, pond of water, building-s, etc. 

Run the line up to a convenient point near 
the obstruction, mark this point and set the 
compass over it. Then with one pair of sig-hts 
directed to a back-stcike, which should not be 
less than ten rods away, measure from the 
point under the compass, in line with the other 
pair of sig-hts, far enoug-h to pass the ol)struc- 
tion and mark the point. Then g-o to the 
back-stake and measure from it in the same 
direction, exactly the same distance, and set 
uj) a stake. Now set the C()m])ass over the 
first offset ])()inl and direct a ])iiir of sig-hts to 
this stake; these sig-hts will then ])e ])arallel to 
the required line. Now continue the measure- 
ment on this offset line far ^'nougli t«> ])asN the 
obstacle; niiirk this point, and another about 



(46) 

ten rods farther on. Set the compass over the 
iirst point and then measure from these two 
points back to the true line in the same 
manner as when leaving- it. Add the Icng-th 
of the offset line to that of the true line, up to 
the point where you left it. 

In order to g^uard ag-ainst error in measure- 
ments, the offset and offset lin:: should each 
terminate with a whole chain. 

There are other methods by which obstruc- 
tions may be passed, but this one is, perhaps, 
the most simple. 

Case 3. Required to run a line the ends of 
which are not visible from each other because 
of intervening- hills. 

Go to some point between, from which both 
ends of the line can be seen and set the com- 
pass on the line, as near as can be guessed, 
and direct a pair of sig-hts to a flag'-staif at one 
end of the line. Then turn and sig-ht in the 
opposite direction, and if a flag-'Staff at the 
other end can be seen, the compass is on the 
line; but if not, the compass must be moved in 
the opposite direction from that side on which 
the line of sight falls. Then direct the sig-hts 
ag-ain to the first staff sig-hted, and again turn 
and sig-ht in the opposite direction; if still cff 
of the line repeat the operation until both flag*- 
staffs can be seen throug-h the sig-hts without 
chang-ing- the position of the compass. Stakes 
can then be set on the line in both directions 
as may be desired. 

Case 4. Required to run a line through 
timbered land a distance of forty chains to a 
corner. 



(-7) 

Suppose this to he the line cHvidin<^ the east 
li'cill" and the west half of the south-west 
ruarter of a section. Beg-innint^- at the south 
line of the quarter y(^u will set the compass 
over the corner, which should he midwa^^ be- 
tween tlie south cjuarter corner and the south 
w ^st corner of the section. If a flag*-staff 
])]aced at either of these corners can be seen 
r:\)m the compasLs place one there and direct 
a pair of sig-lits to it; the other pair should 
th Ml be in the direction of the required line; 
l)ut if neither of these corners are visible from 
the compass, tlun assume a bearing* as near 
due north as can ba judg-ed, and run throug-h 
according- to instructions already g-iven, driv- 
ing- a stake at each ''out." The eig-hth stake 
will be at the corner, or terminus of your line. 
Suppose that upon reaching* the north line of 
the quarter, you find that you have missed the 
corner to which you was running', w^hich you 
will very likely do, and that your random line 
terminates to the left of the corner a distance 
of fifty-six links; the "out stakes'' may now 
be placed on the true line by the following": 

K^IJ^ FOR COK'KM^CTINC; Till-: STAK]-:S. 

Divid? the distance between the termination 
of the random line and true line by the leng'th 
of the line surveyed, and multiply the (pio- 
tient by the number of cliains the stake is 
from the starling- r)oint. This will i^"i\e the 
distance that the stake must ])c uiowmI to tlie 
riiifht or left iis tlu- case ma\- br. 



(48) 

Taking- the above case for example, the 
distance between the termination of the 
two lines, 56 links, divided by the leng-th of 
the line surveyed, 40 chains, g-ives one and 
four-tenths link for the correction for each 
chain. The stakes being- five chains apart 
the correction is make as follows: 

Ik. ch. Ik. 

1.4 X 5= 7=^Correction for 1st Stake. 

1.4X10 = 14:^ '' '' 2d 

1.4X15 = 21= '' '' 3d '' etc. 

1.4X35 = 49= " " 7th 

1.4X40 = 56= '^" '' 8th 

When, as in the above case, the line surv^^ed 
terminates at a stake, it will be necessar}^ only 
to divide the distance missed b}^ the number 
of stakes. Then 56^8 = 7 links for each stake, 
same as above. 

Case 5. Required to run a line which shall 
make an ang-le with another line a g-iven num- 
ber of deg-rees. 

With a compass having- no circle g-raduated 
to deg-rees, this requirement seems unreasona- 
ble. But what is the difference where the 
g-raduated circle is, so we g-et the ang-le? 

Drive a peg- at the point where the ang-le is 
to be made, and let one end of a 33 foot line be 
held at this point, and with a marking- pin at 
the other end, describe an arc of a circle; be- 
g-inning- at the line with which the ang-le is 



(40) 

to be iiicide. Now, the leiig-th of an arc of one 
degree for a radius of 3J; feet is .S759() of a foot. 
Multiply this decimal In- the number of de- 
i>Tees in the an^fle to be made; which will ofive 
the leng-th of the arc. Measure the distance 
on the arc described, and mark the poinL. 
With the compass set over the i>«:^g', direct a 
|)air of sig'hts to this point; then they will be 
in the direction of the required line. Suppose 
the required line is to bear north ten deg-rees 
west, and a'ou have the north line. Drive a 
peg- at the vertex of the ang-le, then with one 
end of the chain held at this point draw the 
other end westw^ard from the north line a dis- 
tance of about six feet, marking- on the g^round 
as you g-o. Now the leng-th of an arc of 10 
deg-rees will be .57596x10-5.75960 feet, or 5 
feet and about 9 '4] inches. Measure this dis- 
tance on the arc from the north line. Then a 
line drawn from the peg- throug-h this point 
will be the required line. For ang-les less than 
a deg-ree, divide the above fraction by the 
g-iven fraction of a deg-ree. 

While the above method for setting- off an- 
g-les is correct in theory, it is not ])ractical 
except w^here the g-round over which the chain 
is to pass in describing' the arc is horizontal, 
or level; and smooth enoug-h that a line line 
may ])e traced with a marking- i)in. The arc. 
which must be a true curve, should be nuas- 
ured with a cord or line that will not stretch, 
laid on the arc. 



(50) 



Case 6. Required to measure a line to a 
point which is inaccessible: as. for instance, 
to the opposite side of a river. 

L-t AB be the line 
and B the point. Then 
with the compass at C. 
let a flag'-staff be set up 
in line at B. ]\Iark the 
points CECt say. six 
rods anart. Make each 
of the lines CD. EF, G 
H a rig'ht-anofle to the 
line AB and mark the 
points DFH about ten 
rods from it. Set up 
the compass at F and 
direct a pair of sig-hts 
to B. Mark the point 
where the line of sig'ht 
cuts the line CD and 
measure exactly its dis- 
tance from C. Meas- 
ure the same distance 
from G on the line GH and mark the point. 
Direct a pair of sig*hts to this point and mark 
the point where the line of si^ht extended 
cuts the line AB, as at I. Then will thedis- 
tan:e IG equal the distance CB. 

For practice tr^' the above where the point 
is accessible, then measure throug*h and com- 
pare results. 




(SI) 

Havino- now had instructions in the use of 
the compass and chain sufficient to cover all 
ordinary cases, before making- use of them in 
dividing- and subdividing- sections, it will be 
necessary to know the manner in which the 
Government lands, or a g-reater part of thtm, 
Avere surveyed. This we wnll notice briefly. 

OKICilNAL SUKVEV. 

The meti who are authorized b}^ the Govern- 
ment to do this important work are sent out 
under written instructions from the surveyor- 
g-eneral, setting- forth the manner in which 
the work shall be done. The first thing the 
surveyor does is to select some permanent, im- 
perishable object, which he establishes as the 
initial point from which to beg-in the survc3\ 
From this point he runs a line east or west, 
or east and west, to the limit of the territory 
to be surveyed; this is called the base line. 
He then runs another line north or south, or 
north and south, to the limit of the survey. 
This is called the principal meridian. These 
two lines, which are surveyed with line in- 
struments and with the utmost care, form the 
basis for the survey of all other lines within 
their limits. Each half-mile of these two lines 
is marked with a monument by setting- a ])ost, 
where there is timber, or where there is none 
by throwing up a mound of earth around a 
stake or stone. From each six-miles point on 
the base line, other meridian lines are sur\ey- 
chI, which divide the territory into stri])s each 
six miles wide. These strii)s ar*.' calK'd ran- 



(52) 

g*2s. The first one west of the principal me- 
ridian is called rang-e 1 west, the second is 
called ran^e 2 west, and so on; the first one 
east is called rangfe 1 east, the second ranofe 
2 ea^^t, etc. These meridian lines are crossed 
by other lines run parallel to the base from 
each six miles point on the principal meridi- 
an. Thus the territory is divided into town- 
ships; each containing- thirt3^-six square miles 
or sections. Each township is numbered or 
named with reference to its distance from the 
base and principal meridian; thus, township 
23 north, rang-e 10 east, means that it is the 
twenty -third townshiff north of the base line 
and of the tenth rang-e east of the principal 
meridian. 

The law provides that east and west boun- 
daries of townships are always to be run from 
south to north on a true meridian line, and 
since meridian lines all come tog-ether at the 
poles, it is plain that a township north must 
be somewhat narrower than the one south of 
it, and in order that they may all be about the 
same in area, lines called standard parallels 
are surveyed every four townships north of 
the base line and every five townships south 
of it and alwa^'s parallel to it. Upon these 
lines the distances are set off anew as on the 
base line. Auxiliary meridians are also sur- 
veyed every eig-ht townships east and west of 
the principle meridian, but descriptions are 
all referred to the base and principle meridi- 
an lines just as though these did not exist. 



(33) 

The townships contain thirty-six sections 
each, which are numbered beg-inning- with 
number one in the north-east corner and num- 
bering- west to six, then with seven south of 
six, number east to twelve; and so on to thir- 
ty-six in the south-east corner of the township. 
From the time the surveyor beg-ins until the 
townships are laid out in sections he marks 
every haif-mile of true line he surveys, in the 
manner as before stated; and when timber is 
near he marks two or more trees as witnesses, 
g-iving the kind of tree, its diameter in inches 
and its course and distance from the corner; a 
copy of which is usually recorded in each 
county. These, together with similar notes 
taken by the county surveyor, make up the 
surveyor's records of field-notes in each county. 

The manner in which the sections are sur- 
veyed are as follows: The surveyor begins at 
the south-west corner of section 36 and runs 
north, parallel to the east line of the town- 
ship. At 40 chains he establishes the quarter- 
section corner between sections 35 and 36; he 
then runs 40 chains farther where he estab- 
lishes the corner to sections 25, 26, 35 and 3(). 
From this point he runs a random line east to 
the township line. If he misses the corner on 
the townshiT> line, he corrects back and sets 
the quarter-section corner on the true line be- 
tween sections 25 and 3(). an e(|ual distance 
between the section corners. Keturning to 
the south-west corner of section 25, he ]>ro- 
ceedr. in the saniL' wa\- to sur\c\- that section; 



(5U 

and so continues until he reaches the north 
line of the township. He then returns to the 
south line, and beg-innin^ at the south-west 
corner of section 35, he proceeds to survey the 
next tier of sections in the same way; by run- 
ning* first north then east, closing- each time 
on the section corners just previously estab- 
lished. The last two tiers of sections are sur- 
veyed tog-ether, by running- first north then 
east, then west to the west line of the town- 
ship. 

There are two sets of corners established on 
correction parallels, one for sections south and 
one for sections north' of the line. Besides 
these it is not uncommon to find two sets on 
other township lines; for the reason that in 
running- the section lines north and west to 
the north and west boundary lines of the 
township, they were not made to close on the 
corners previously established on those lines: 
and therefore offsets frequently occur at every 
mile on township lines except at township 
corners. 

For reasons already stated, townships can 
not be quite square, consequently some sec- 
tions must fall short; therefore the law pro- 
vides that the excess or deficiency shall fall 
on the last half-mile of the north and west 
tiers of sections. These are called fractional 
sections. There are many other thing's relat- 
ing* to the survey of the public lands, but the 
foreg-oing* will be sufficient for our purpose. 
Subsequent survey's prove that many errors in 



(55) 

the orig-inal have been made, but none of the 
lines or corners can be chang-ed. It is there- 
fore the duty of the county or other surveyor, 
when dividing- and subdividing- sections, to 
follow as closel}' as possible the orig-inal sur- 
vey. If these surveys had been made on the 
g-round as we see them represented on paper, 
it would be a comparatively easy matter to 
follow them. But to the contrary, we find that 
section lines seldom run east and west, north 
and south. That they bend at nearly every 
lialf-mile, and that the quarter-section corners 
are seldom equi distant between the section 
corners. By reason of this some quarters in 
the same section are made to overrun and oth- 
ers fall short. But they are all sold as con- 
taining one hundred and sixty acres each, 
except the fractional quarters in the north 
and west tiers of sections, which are sold as 
containing whatever the Government survey- 
ors returns show. 

SUBDIVISIONS OF SECTIONS AND METHOD OK 
ESTABLISH I N(; COKNEKS. 

As before stated the four corners of a sec- 
tion, and the corners between them called 
([uarter-section corners, are established by the 
county or other surveyor, in accordance with 
these corners. The ])rinci])al lines to be sur- 
veyed in subdividing sections are those which 
divide the (juarters into eighty, forty, twenty 
and ten acre tracts. The method of establish- 
inu" the corners to these tracts will now \)c 



(56) 

considered; presuming* that all of the original 
corners can be found, and that the center cor- 
ner of the section has been previously' estab- 
lished. This, however, is done by running 
lines crossing the section each way from the 
quarter corners and placing- the corner at the 
intersection of the lines. 

To divide a quvirter section into eighty acre 
tracts. 1. By a line running- north and south. 
Suppose it to be the south-east quarter. Run 
a line from the east quarter corner to the cen- 
ter of the section, and place the corner on the 
middle of the line. Then run a line from the 
south-east corner of the section to the south 
quarter corner, and set the corner on the mid- 
dle of the line. Then a line connecting- these 
two corners will be the required line. 2. By 
a line running- east and west. Run a line from 
the south quarter corner to the center of the 
section, and from the south-east corner to the 
east quarter corner, and set the corners on the 
middle of the lines. 

To divide the quarter=section into forty acre 
tracts. Establish a corner on each of the 
boundary lines of the quarter by the above 
method, then run lines connecting- these cor- 
ners, crossing- the quarter each way, and set a 
corner at the intersection of the lines. 

To divide the quarter into twenty and ten 
acre tracts. This division is not likely to oc- 
cur. But, havintr established the corners to 



the forty acre tracts, you will proceed to di- 
vide them into ten and twenty acre tracts in 
the same manner as the quarter was divided 
into eig-hty and forty acre tracts; by taking- 
the middle of their boundary lines for the 
corners. 

The same rules will apply to all the quar- 
ters in the township, except those bounded on 
the north and west by the township lines; and 
a few others made fractional by lakes, rivers, 
indian reservations, etc. 

As there are frequently no quarter-section 
cornets on the north and west sides of sections 
bounded on the north and west by township 
lines, and the work of dividing- the fractional 
quarters being- somewhat complicated, this 
w^ork will be left to the count}^ surveyor. The 
re-location of corners will also be left to ex- 
perienced men. Nor is it advisable for any 
other person to make excavations in search for 
a corner, unless it is known that a stone has 
been deposited or a stake recently driven to 
mark the corner; for the reason that certain 
recog-nizable evidences of the location of a cor- 
ner would be passed by unnoticed and perha])s 
destroyed b)' any other than an experienced 
person. If the witness trees and all traces of 
a corner have disappeared, it is impossible in 
most cases to re-locate an ori^:final corner; even 
the surveyor who established it would fail. It 
is therefore of g-reat importance to land own- 
ers that these corners be ])er])ctiiate(l. 



(58) 



TABLE FOR LAND MEASURE. 

7.92 inches=l link marked Ik. 
100 links =1 chain '' cli.=:66 feet. 
80 chains =^1 mile '* mi. 
25 link =1 rod '' rd.=:16V2 ft. 

16squraerods = l square chain sq. ch. 
10 *' chains = l acre A. 

160 " rods =1 acre 
43560 '* feet =1 acre 

Chains and links are expressed the same and 
calculated in the same manner as dollars and 
cents. Five chains and six links, multiplied 
b\^ three chains and sixteen links, would be 
expressed and multiplied thus: 5.06x3.16 = 
15.9896 ch. 

Any number of links less than one hundred 
are expressed as hundredths of a chain. One 
link is expressed thus, .01; ninety links thus, 
.90. Also the fractions ^. ^, ;/(, etc. for con- 
veniencY are expressed decimally thus, .75, 
.50, .25.' 

To j-rfliLce chains to feet. — Multiply by 66. 
How many feet in 3.16 chains? 

3.16X66 = 208.56 feet. 
In 50 links? .50x66= 33.00 feet. 

To reduce feet to cliains. — Divide by 66. 
How^ many chains in 82 >2 feet? 
82.50^66 = 1.25 ch. 
In 8 feet and 3 inches? 8.25-^66 = .125 ch. 



(59) 

To reduce chains to rods. — Multiply bv 4. 
How many rods in 3.25 chains? 

3.25x4^:13.00 rods. 
In 4.22 chains? 4.22x4 = 16.^8 rods. 
In 12'j links? ,125x4= .50 rods. 

To reduce rods to cluiins. — Divide hy 4. 
How many chains in 18 rods? 

18.00^4 = 4.50 ch. 
In 7>2 rods? 7.50-^-4=1.875 ch. 
In 3 rods? 3.00-^4=.75 ch. 

COMPUTATION OF AREA. 

In computing- areas the work may be short-' 
ened by expressing- the leng-th of all the lines 
in chains and hundredths of a chain. In mul- 
tiplying the leng-ths of lines containing- hun- 
dredths of a chain one by another, point off 
from the rig-ht of the product as may figures 
for decimals as there are decimals in both 
multiplicand and multiplier. Divide by 10 for 
the acres by moving* the decimal point one 
place to the left. 

To find the (trefi of (f jxi rol 1 el o^ra nt oi' rec- 
to n ^le. 

Rule. — Multiply the leng-th in chains by the 
perpendicular breadth in chains for the square 
chains, and divide by 10 for the acres. 

1. How many acres in a parallelogram; the 
length 30 chains, and the per])en(licular 
breadth 21 chains? 

Solution. 30X21=630 scj. ch. 
630^10= ()3 acres. 



(601 

2. How many acres in a rectang-ular lield 
8*75 chains long- bv 5 chains wide. 

S:)lution. S.75X - 5^=43.75 sq. ch. 
43.75-^-10=4.375 A. 

3. In a square field, each side of which is 
15.75 chains, how many acres? 

Solution. 15.75x1^.75 =248.0625 sq.ch. 
248. 0h25-^ln =24.80625 A. 

After finding- the area of an entire tract, 
when as in the above example there are sev- 
eral decimal fig-ures. we usually cut off all but 
two: adding- 1 to the ^cond fig-ure when the 
third is more than 5. In the above area the 
third decimal fig-ure is 6; adding 1 to the sec- 
ond figure, we have for the area 24.81 A. 

To find file area of a triidJe. 
For right-angle triangles, or triangles 
whose perpendicular hight is g-iven. 

Rule. — Multiply the base by the perpendic- 
ular hight. and take half the product for the 
area. 

1. Yiow many acres in a triang-ular piece of 
land: the base 11 chains, the perpendicular 
hight 4.50 chains? 

Solution. 11x4.50=49.50 sq. ch. 
4*^). 50 -f- 10=4. 950 
4.950^2=2.475 A. 

2. How manv acres in a triangular field: 
the base 20 chains, and the perpendicular. 
lfi.75 chains? 



(61) 

Solution. 20X16.75^-335.00 sq. ch. 
335.00-^10-^33.50 
33.50-^2=:^ 16.75 A. 

(I 7/r// flic sides onl ij a re ^i rcif. 

Rule. 1. Add the three sides tou^-ether, and 
tiike half the sum. 

2. From the half sum take the three sides 
severally. 

3. Multiply the half sum and three remain- 
ders tog-ether. 

4. Extract the scjuare root of the product 
for the area. 

How many acres in a triangular held, the 
sides of which are 13, 14 and 15 chains, re- 
spectively? 

Solution. 13+ 14 + 15 —-42, sum of the 3 sides. 
42-f- 2=21, the half sum. 
21 13= 8, 1st remainder. 
21 14= 7, 2d 
21 15= 6, M\ 

21 X8X 7X6 = 7056 
^ 7056 = 84 sq. ch. 

84-^10=8.4 acres. 

The area of a held or piece of land in any 
lig-ure may be found by dividing- it into trian- 
g-les, and C()m])uting- the area of each, sepa- 
rately. The sum of the areas of all the trian- 

i>-les will be the area of the tract. 



(62) 



DIVISION OF LAND. 



To lay down rules covering- all cases that 
mig-ht come up, would require more space than 
is allotted to this work; therefore only a few 
cases of most common occurrence will be given. 

Case 1. — To divide a rectangle into any num- 
ber of shares, by lines running' parallel to a 
side, so that the shares will be to each other 
as their representative numbers, or parts. 

Rule. — Divide the base lines by the numer- 
ators or numbers representing* the several 
shares, and multiph^ the number representing- 
each share by the quotient thus obtained. Or 
put the number of acres in place of the base 
line when the acres are required. 

Problem 1. — Divide the south half of a quar- 
ter-section into 5 shares, by lines running 
north and south, so that the shares will be to 
each other as 1, 2, 3, 5 and 5; the length of 
the base line being- 40 chains. 

1+2+3+5+5=^16, and 16 = 40. 

40-^16=: 2.50 = least part. 
2.50X 1= 2.50 chains, =lst share. 
2.50X 2= 5.00 chains, -= 2d 
2.50X 3= 7.50 chains, =3d 
2.50X 5 = 12.50 chains, = 4th 
2.50X 5=12.50 chains. =5th 
"40^ 

Prob. 2. — Divide 66 acres between three 
persons; A, B and C; giving to A, 2-10; to B, 
3-10 and to C, 5-10. 



(0)3) 

2+3+5=10.==66. 
f)f)— l()=6.6=rleast share. 
().(>X 2 = 13.2 acres=A's share. 
().(>X 3=19.8 acres = B's 
f).f)X S = 33. acres = C's '' 

Case 2. The area and one side of a rectan- 
i^ie l)ein<^" i>*iven, to find the other side. 

Rule. Divide the area by the g*iven side; 
the quotient will be the other side. 

Prob. 1. -One side of a rectang-ular field is 
30.5 rods; what will be the leng-th of the other 
side for 4 ' - acres? 

lf)()X4.5i)--72() sq. rd.=area 

720^30. 5=23. () rd. Ans. 

Prob. 2. - A field 24 chains lon^j;- contains 
21 acres; wdiat is its width? 

21 X 10=210 sq. ch.z=area. 
210^24 = 8.75 chains. Ans. 

Case 3. "-The area of a square field being* 
i^iven, to tind its sides. 

Rule. — Kxtract the square root of the area. 

Prob. 1. -A square field contains 22 ^1.' acres; 
what is the leng-th of each side? 

l()OX22.50 = 3()00 sq. rd.=area. 
s3f)00---f)0 rods. Ans. 

Prol). 2. What will l)e the sides of a scjuart.' 
i\v\i\ that shall contain 3 acres? 



(64) 

3X10=30 sq. ch. 
V 30—5.478 chains. Ans. 

How many rods of fence will be required to 
fence in 1 acre? 

If but 1 rod wide, it will require 322 rods; 
but if square, a little more than SO^A rods will 
fence it. 

The above is g-iven to show that there is 
economy in fencing- g-round in a square form 
when it can be done. 

Case 4. — From a rig-ht-ang-led triangle, to 
cut off a g-iven number bf acres, by a line per- 
pendicular to the base. 

Rule. — I.Divide the perpendicular of the 
whole triang-le by its base. 

2. Take any leng-th of base, less than the 
required base, and multiply it by the above 
quotient; which will give its perpendicular. 

3. Compute the area of this triangle. 

4. Multiph^ the square of its base by the 
required area, and divide the product by the 
computed area; which will give the square of 
the base sought. 

5. Extract the square root of this square; 
which will give the base of the required area. 
Having the base, the perpendicular may be 
found by multiplying this base by the quo- 
tient obtained in the first above proceeding. 

The base must be measured from the end 
opposite the foot of the perpendicular. 



(65) 

Note. —When the part to be cut off is next 
the perpendicular, subtract it from the area 
of the whole trian^ie, and find the base and 
])erpendicular of the remainder. 

Problem 1. P^rom a rigdit-angded trian^ie 
whose base is 8 chains, and j)rependicular 
chains; to cut off 1 ^2 acres. 

(I ) ().()()-^8,00 -.75 — equal perpendicular for 

each chain of base. 

(2 ) 2.00 chains, assumed base. 

{'') 2. 00 X. 75- 1.50 ch.:= perpendicular. 

(3 ) 2.00X1.50 = 3.00 sq. ch. 

(^•) 3.00^lO-=.30 = d()uble area. 

('') .30-^ 2 = .15 of an acre in triani^le. 

( 4 ) 2.00 X 2.00==4.00=square of assumed base 

('') 4.00 X 1.50=:::().0() 

( *') ().00-^.15=40 = square of required base. 
(5 ) \ 40 ^()- 324 chains. Ans. 

The area of the whole triang-le is 2.4 acres. 
Now, if it was required to cut off .^) of an acre 
next the perpendicular, since the remainder 
would be I'j acres the process, according- to 
the above note, would be the same; and the 
leng-th of the base would be 8.00— 6.324= 1.676 
chains; and the length of the per])endicular 
would be 6. 324 X. 75=4. 742 ch. 



(66) 



ABSTRACT OF DECISIONS 

OF 

VARIOUS STATE COURTS, 

WITH REFEKEXCE TO SURVEYS, ETC, 



1. Visible monuments, control courses and 
distances. 

The Buffalo, etc., K. R. Co. vs. Stig-eler, (A 
N. Y. 348. 

Pitcher vs. Dove, 99 Ind. 175. 

2. A g-rantor referred to a g-overnment cor- 
ner as a monument in the description of land 
in a deed, but mistook the location of the g*ov- 
ernment line, which he intended to mark the 
northern boundar^^ of the land conveyed. The 
land laid off was marked by stakes and other 
monuments, and was conve^^ed with reference 
to such boundaries. 

Held, that the g-rantee took the land accord- 
ing* to the lines actually run and established, 
thoug-h they did not correspond to the line in 
the g-overnment survey-. 

Same. When a deed describes land by meas- 
urements, and at the same time b}^ known and 
visible monuments, the latter will g-overn the 
call for courses and distances. 



(67) 

Same. The rule of applying* descriptions of 
boundaries is(l)to natural objects; (2) to arti- 
ficial marks; and (3) to courses and distances 
<4'iven. 

Fisher and others vs. Bennehoff, (111.) 13 
N. E. Reporter 150. Shepherd vs. Nave and 
others, 125. Ind. 226. Thomas vs. Patten, 13 
Me. 32^). 

3. In construing- a description of land con- 
veyed in a deed, monuments control, then 
courses and distances, and lastly, in their ab- 
sence, the designated quantit^^ will prevail. 
Allen vs. Kersey, (Ind.) N. E. Rep. 557. 

4. A line is to be extended to reach a boun- 
dary in the direction called for, disreg-arding 
the distance. Witherspoon vs. Blanks, 1 Tay- 
lor (N. C. ) 110. 

5. A survey of lands establishing corners 
and lines made in accordance with the stat- 
utes reg-ulating- the same is conclusive evi- 
dence of such corners and lines unless the sur- 
vey is appealed from as provided by such 
statute. Herbest and others vs. Smith, 71 Ind. 
44. Grover vs. Paddock, 84 Ind. 244. 

(). TliL corners estaldished by the original 
surveyors i)f public lands under the authority 
of the United States, are conclusive as to the 
boundaries of sections and divisions thereof, 
and no error in placing them can be corrected 
by any surxey made by individuals or bv a 
state sur\evor. Arnier \s. Wallace, 2S Miss. 55<) 



(68) 



ADVERSE POSSESSION. 



7. Where adjoining- land owners cause the 
division line between them to be surve^^ed and 
established, such survey conclusivelv estab- 
lishes such line, and is binding* alike upon 
them and all who claim under them. 

Same. — When such proprietors ag-ree upon 
a division line, and one take possession and 
occupies the land to such line, peaceably- and 
undisturbed, under claim of title, for more 
than twenty years, such j)ossession divests the 
other of an}' title that he may have had to the 
land so occupied. 

Same. — When parties ag-ree upon such line, 
and each occupies to such line for more than 
twenty years, such ag-reement and occupancy 
g-ive title to the line without reference to the 
true line. Main vs. Killing-er, 90 Ind. 165. 
Smith vs. McKay, 30 Ohio St. 409. Fahey vs. 
Marsh, 40 Mich. 236. Whitman vs. Henneber- 
ry, 73 111. 109. 

8. Where for more than twenty years a per- 
son and his g-rantors have continuously and 
uninterruptedlv occupied land extending* to a 
fence built by his remote g-rantor, claiming* 
throughout that it was the dividing* line, 
and using* and cultivating* such land, under a 
continuous claim of ownership, he becomes 
the owner in fee, and ejectment will not lie 
ag-ainst him bv one having* the paper title. 
Rig*g*s vs. Riley, (Ind. ) 15 X. E. 253. 



im 



LANDS BOUNDED ON vSTKKKTS OK IIKUIWAVS. 

9. Conveyance of lands adjoining- a public 
highway conveys the fee to the center of the 
hig-hway, unless the deed otherwise provides. 
Cox vs. R. R. Co., 48 Ind. 178. R. R. Co. vs. 
Scott, 74 Ind. 29. 

10. Where the lines of a deed calls for a pub- 
lic road, the owner is entitled to hold to the 
middle of the road, and the fact that the road 
is subsequently vacated will not deprive the 
g-rantee of such owner of his rig-hts in the 
road. Ott vs. Kreiter, (Pa.) 1 Atl. Rep. 724. 

11. A deed describing* the g-ranted land as ly- 
ing- ''southwardly of a hig-hway," and ''except- 
ing- the road laid out over said land," must be 
construed as conve3ang- the land to the center 
of the hig-hway, subject to the pi^blic rig-ht of 
way. Wellman vs. Dickey, (Me.) 2 Atl. Rep. 
133. 

12. A deed of a lot bounded by stones "on 
the side of a road," and answering- the call for 
quantity, without including- the road, does not 
convey to the center of the road. Peabody 
Heig-hts Co. vs. Sadtler, 63 Md. 533. 

13. Where, in a deed, land is bounded on a 
street, or its boundary line runs to a street, 
and thence by the street, the g-rantee takes to 
the middle of the street, unless the deed, or 
the character of the locality to which it is to 
be api)lied, indicates a different intention of 
the parties. Hamlin vs. Pairpont Manf'g* Co. 
(Mass.) N. E. Rep. 531. 



(70) 



14. The grantee of a lot bounded by a pub- 
lic street in a recorded town plat, whether the 
lot is desig-nated by numbers, or described by 
metes and bounds, takes to the center of the 
street, unless expressly excluded b}^ the g-rant. 
Kneeland vs. Van Valkenburg-h, (Wis.) 1 N. 
E. Rep. 63. 

15. The office of a description in a deed is 
not to identify the land conveyed, but to furn- 
ish the means of identification. Rucker vs. 
Steelman, 73 Ind. 396. Scheible vs. Slag-le, 
89 Ind. 323. Colcord vs. Alexander, 67 111. 
581. Slater vs. Breece, 36 Mich. 77. 



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